結果

問題 No.3154 convex polygon judge
ユーザー PNJ
提出日時 2025-05-20 21:47:33
言語 C++23
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 207 ms / 2,000 ms
コード長 12,286 bytes
コンパイル時間 3,683 ms
コンパイル使用メモリ 296,384 KB
実行使用メモリ 16,224 KB
最終ジャッジ日時 2025-05-20 21:47:40
合計ジャッジ時間 6,648 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 44
権限があれば一括ダウンロードができます

ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;

template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;

#define vv(type, name, h, w) vector<vector<type>> name(h, vector<type>(w))
#define vvv(type, name, h, w, l) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(l)))
#define vvvv(type, name, a, b, c, d) vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(d))))
#define vvvvv(type, name, a, b, c, d, e) vector<vector<vector<vector<vector<type>>>>> name(a, vector<vector<vector<vector<type>>>>(b, vector<vector<vector<type>>>(c, vector<vector<type>>(d, vector<type>(e)))))

#define elif else if

#define FOR1(a) for (long long _ = 0; _ < (long long)(a); _++)
#define FOR2(i, n) for (long long i = 0; i < (long long)(n); i++)
#define FOR3(i, l, r) for (long long i = l; i < (long long)(r); i++)
#define FOR4(i, l, r, c) for (long long i = l; i < (long long)(r); i += c)
#define FOR1_R(a) for (long long _ = (long long)(a) - 1; _ >= 0; _--)
#define FOR2_R(i, n) for (long long i = (long long)(n) - 1; i >= (long long)(0); i--)
#define FOR3_R(i, l, r) for (long long i = (long long)(r) - 1; i >= (long long)(l); i--)
#define FOR4_R(i, l, r, c) for (long long i = (long long)(r) - 1; i >= (long long)(l); i -= (c))
#define overload4(a, b, c, d, e, ...) e
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload4(__VA_ARGS__, FOR4_R, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_in(a, A) for (auto a: A)
#define FOR_each(a, A) for (auto &&a: A)
#define FOR_subset(t, s) for(long long t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))

#define all(x) x.begin(), x.end()
#define len(x) int(x.size())

int popcount(int x) { return __builtin_popcount(x); }
int popcount(uint32_t x) { return __builtin_popcount(x); }
int popcount(long long x) { return __builtin_popcountll(x); }
int popcount(uint64_t x) { return __builtin_popcountll(x); }
// __builtin_clz(x)は最上位bitからいくつ0があるか.
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(uint32_t x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(long long x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(uint64_t x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }

// 入力
void rd() {}
void rd(char &c) { cin >> c; }
void rd(string &s) { cin >> s; }
void rd(int &x) { cin >> x; }
void rd(uint32_t &x) { cin >> x; }
void rd(long long &x) { cin >> x; }
void rd(uint64_t &x) { cin >> x; }
template<class T>
void rd(vector<T> &v) {
  for (auto& x:v) rd(x);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

#define CHAR(...) \
  char __VA_ARGS__; \
  read(__VA_ARGS__)

#define STRING(...) \
  string __VA_ARGS__; \
  read(__VA_ARGS__)

#define INT(...) \
  int __VA_ARGS__; \
  read(__VA_ARGS__)

#define U32(...) \
  uint32_t __VA_ARGS__; \
  read(__VA_ARGS__)

#define LL(...) \
  long long __VA_ARGS__; \
  read(__VA_ARGS__)

#define U64(...) \
  uint64_t __VA_ARGS__; \
  read(__VA_ARGS__)

#define VC(t, a, n) \
  vector<t> a(n); \
  read(a)

#define VVC(t, a, h, w) \
  vector<vector<t>> a(h, vector<t>(w)); \
  read(a)

//出力
void wt() {}
void wt(const char c) { cout << c; }
void wt(const string s) { cout << s; }
void wt(int x) { cout << x; }
void wt(uint32_t x) { cout << x; }
void wt(long long x) { cout << x; }
void wt(uint64_t x) { cout << x; }
void wt(double x) { cout << fixed << setprecision(16) << x; }
void wt(long double x) { cout << fixed << setprecision(16) << x; }

template<class T>
void wt(const vector<T> v) {
  int n = v.size();
  for (int i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(v[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

/////////////////////////////////////////////////////////////////////////////////////////
long long min(long long a, long long b) { return a < b ? a : b; }

template <class T>
T min(vector<T> A) {
  assert (A.size());
  T S = A[0];
  for (T a : A) S = min(a, S);
  return S;
}

long long max(long long a, long long b) { return a > b ? a : b; }

template <class T>
T max(vector<T> A) {
  assert (A.size());
  T S = A[0];
  for (T a : A) S = max(a, S);
  return S;
}

long long add(long long x, long long y) {return x + y; }

template <class mint>
mint add(mint x, mint y) { return x + y; }

template <class T>
bool chmin(T & x, T a) { return a < x ? (x = a, true) : false; }

template <class T>
bool chmax(T & x, T a) { return a > x ? (x = a, true) : false; }

template <class T>
T sum(vector<T> A) {
  T S = 0;
  for (int i = 0; i < int(A.size()); i++) S += A[i];
  return S;
}

uint64_t random_u64(uint64_t l, uint64_t r) {
  static std::random_device rd;
  static std::mt19937_64 gen(rd());
  std::uniform_int_distribution<uint64_t> dist(l, r);
  return dist(gen);
}

long long gcd(long long a, long long b) {
  while (a) {
    b %= a;
    if (b == 0) return a;
    a %= b;
  }
  return b;
}

long long lcm(long long a, long long b) {
  if (a * b == 0) return 0;
  return a * b / gcd(a, b);
}

long long pow_mod(long long a, long long r, long long mod) {
  long long res = 1, p = a % mod;
  while (r) {
    if ((r % 2) == 1) res = res * p % mod;
    p = p * p % mod, r >>= 1;
  }
  return res;
}

long long mod_inv(long long a, long long mod) {
  if (mod == 1) return 0;
  a %= mod;
  long long b = mod, s = 1, t = 0;
  while (1) {
    if (a == 1) return s;
    t -= (b / a) * s;
    b %= a;
    if (b == 1) return t + mod;
    s -= (a / b) * t;
    a %= b;
  }
}

long long Garner(vector<long long> Rem, vector<long long> Mod, int MOD) {
  assert (Rem.size() == Mod.size());
  long long mod = MOD;
  Rem.push_back(0);
  Mod.push_back(mod);
  long long n = Mod.size();
  vector<long long> coffs(n, 1);
  vector<long long> constants(n, 0);
  for (int i = 0; i < n - 1; i++) {
    long long v = (Mod[i] + Rem[i] - constants[i]) % Mod[i];
    v *= mod_inv(coffs[i], Mod[i]);
    v %= Mod[i];
    for (int j = i + 1; j < n; j++) {
      constants[j] = (constants[j] + coffs[j] * v) % Mod[j];
      coffs[j] = (coffs[j] * Mod[i]) % Mod[j];
    }
  }
  return constants[n - 1];
}

long long Tonelli_Shanks(long long a, long long mod) {
  a %= mod;
  if (a < 2) return a;
  if (pow_mod(a, (mod - 1) / 2, mod) != 1) return -1;
  if (mod % 4 == 3) return pow_mod(a, (mod + 1) / 4, mod);

  long long b = 3;
  if (mod != 998244353) {
    while (pow_mod(b, (mod - 1) / 2, mod) == 1) {
      b = random_u64(2, mod - 1);
    }
  }

  long long q = mod - 1;
  long long Q = 0;
  while (q % 2 == 0) {
    Q++, q /= 2;
  }

  long long x = pow_mod(a, (q + 1) / 2, mod);
  b = pow_mod(b, q, mod);

  long long shift = 2;
  while ((x * x) % mod != a) {
    long long error = (((pow_mod(a, mod - 2, mod) * x) % mod) * x) % mod;
    if (pow_mod(error, 1 << (Q - shift), mod) != 1) {
      x = (x * b) % mod;
    }
    b = (b * b) % mod;
    shift++;
  }
  return x;
}

/////////////////////////////////////////////////////////////////////////////////////////
// https://nyaannyaan.github.io/library/geometry/geometry-base.hpp
// https://nyaannyaan.github.io/library/geometry/polygon.hpp
using Real = long double;
constexpr Real EPS = 1e-10;
constexpr Real pi = 3.141592653589793238462643383279L;
bool equals(Real a, Real b) { return fabs(b - a) < EPS; }
int sign(Real a) { return equals(a, 0) ? 0 : a > 0 ? 1 : -1; }

template <typename R>
struct PointBase {
  using P = PointBase;
  R x, y;
  PointBase() : x(0), y(0) {}
  PointBase(R _x, R _y) : x(_x), y(_y) {}
  template <typename T, typename U>
  PointBase(const pair<T, U>& p) : x(p.first), y(p.second) {}

  P operator+(const P& r) const { return {x + r.x, y + r.y}; }
  P operator-(const P& r) const { return {x - r.x, y - r.y}; }
  P operator*(R r) const { return {x * r, y * r}; }
  P operator/(R r) const { return {x / r, y / r}; }

  P& operator+=(const P& r) { return (*this) = (*this) + r; }
  P& operator-=(const P& r) { return (*this) = (*this) - r; }
  P& operator*=(R r) { return (*this) = (*this) * r; }
  P& operator/=(R r) { return (*this) = (*this) / r; }

  bool operator<(const P& r) const { return x != r.x ? x < r.x : y < r.y; }
  bool operator==(const P& r) const { return x == r.x and y == r.y; }
  bool operator!=(const P& r) const { return !((*this) == r); }

  P rotate(R rad) const {
    return {x * cos(rad) - y * sin(rad), x * sin(rad) + y * cos(rad)};
  }

  R real() const { return x; }
  R imag() const { return y; }
  friend R real(const P& p) { return p.x; }
  friend R imag(const P& p) { return p.y; }
  friend R dot(const P& l, const P& r) { return l.x * r.x + l.y * r.y; }
  friend R cross(const P& l, const P& r) { return l.x * r.y - l.y * r.x; }
  friend R abs(const P& p) { return sqrt(p.x * p.x + p.y * p.y); }
  friend R norm(const P& p) { return p.x * p.x + p.y * p.y; }
  friend R arg(const P& p) { return atan2(p.y, p.x); }

  friend istream& operator>>(istream& is, P& p) {
    R a, b;
    is >> a >> b;
    p = P{a, b};
    return is;
  }
  friend ostream& operator<<(ostream& os, const P& p) {
    return os << p.x << " " << p.y;
  }
};
using Point = PointBase<long long>;
using Points = vector<Point>;

// ccw, 点の進行方向
int ccw(const Point& a, const Point& b, const Point& c) {
  Point x = b - a, y = c - a;
  if (cross(x, y) > EPS) return +1;                 // 反時計回り
  if (cross(x, y) < -EPS) return -1;                // 時計回り
  if (min(norm(x), norm(y)) < EPS * EPS) return 0;  // c=a または c=b
  if (dot(x, y) < EPS) return +2;                   // c-a-b の順で一直線
  if (norm(x) < norm(y)) return -2;                 // a-b-c の順で一直線
  return 0;                                         // a-c-b の順で一直線
}

using Polygon = vector<Point>;

// 多角形の内部に点があるか？
// OUT : 0, ON : 1, IN : 2
int contains_polygon(const Polygon &Q, const Point &p) {
  bool in = false;
  for (int i = 0; i < (int)Q.size(); i++) {
    Point a = Q[i] - p, b = Q[(i + 1) % Q.size()] - p;
    if (imag(a) > imag(b)) swap(a, b);
    if (sign(imag(a)) <= 0 && 0 < sign(imag(b)) && sign(cross(a, b)) < 0)
      in = !in;
    if (equals(cross(a, b), 0) && sign(dot(a, b)) <= 0) return 1;
  }
  return in ? 2 : 0;
}

// 多角形の面積
Real area(const Polygon &p) {
  Real A = 0;
  for (int i = 0; i < (int)p.size(); ++i) {
    A += cross(p[i], p[(i + 1) % p.size()]);
  }
  return A * 0.5;
}

// 頂点集合から凸包を生成
// boundary : 周上の点も列挙する場合 true
template <bool boundary = false>
Polygon convex_hull(vector<Point> ps) {
  sort(begin(ps), end(ps));
  ps.erase(unique(begin(ps), end(ps)), end(ps));
  int n = ps.size(), k = 0;
  if (n <= 2) return ps;
  vector<Point> ch(2 * n);
  // 反時計周り
  Real th = boundary ? -EPS : +EPS;
  for (int i = 0; i < n; ch[k++] = ps[i++]) {
    while (k >= 2 && cross(ch[k - 1] - ch[k - 2], ps[i] - ch[k - 1]) < th) --k;
  }
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--]) {
    while (k >= t && cross(ch[k - 1] - ch[k - 2], ps[i] - ch[k - 1]) < th) --k;
  }
  ch.resize(k - 1);
  return ch;
}

// 凸包の内部に点があるか？
// OUT : 0, ON : 1, IN : 2
int contains_convex(const Polygon &C, const Point &p) {
  int N = C.size();
  auto b1 = cross(C[1] - C[0], p - C[0]);
  auto b2 = cross(C[N - 1] - C[0], p - C[0]);
  if (b1 < -EPS or b2 > EPS) return 0;
  int L = 1, R = N - 1;
  while (L + 1 < R) {
    int M = (L + R) / 2;
    (cross(p - C[0], C[M] - C[0]) >= 0 ? R : L) = M;
  }
  auto v = cross(C[L] - p, C[R] - p);
  if (equals(v, 0)) {
    return 1;
  } else if (v > 0) {
    return equals(b1, 0) or equals(b2, 0) ? 1 : 2;
  } else {
    return 0;
  }
}

void solve() {
  Points P;
  INT(N);
  FOR(N) {
    LL(X, Y);
    Point p(X, Y);
    P.push_back(p);
  }
  Polygon poly = convex_hull<false>(P);
  string ans = "Yes";
  if (int(poly.size()) != N) ans = "No";
  print(ans);
}

int main() {
  //INT(T);
  FOR(1) solve();
}
0